To build a call center that supports warm transfers, you need to set up an environment using Twilio's Java helper library and Apache Tomcat server. You'll create a servlet called `TwilioCallerServlet` that will handle incoming calls and return TwiML instructions according to the caller. The servlet will check if any key presses were made by the first agent (Artemis) after disconnecting from the conference, and if so, it will make a call to the second agent (Barnabas). If no input was sent, it will check where the incoming call is coming from and handle it accordingly. You'll also need to define constants for your Twilio account SID, authentication token, and servlet mapping URL. Finally, you'll configure your Twilio phone number to reach out to your `TwilioCallerServlet` servlet, and test out your application by having someone call your Twilio number.